Recently [1]} the author gave an interpretation of the Prudnikov sequence of orthogonal polynomials with the weight function \(x^\alpha \rho _\nu (x)\) , where  \( \rho _{\nu }(x)= 2 x^{\nu /2} K_\nu (2\sqrt{x}),\ x >0, \nu \ge 0,\ \alpha > -1\)  and \(K_\nu (z)\)  is the modified Bessel function [2]}, Vol. II, in terms of the so-called composition orthogonality with respect to the measure \(x^\nu e^{-x} dx\)  related to the Laguerre polynomials [3]}. Our main goal here is to characterize a two-parameter sequence of orthogonal polynomials \(\lbrace P_n( x; \lambda , t)\rbrace _{n\ge 0}\)  with respect to the weight function \(x^\alpha e^{- \lambda x} \rho _\nu (x t),\ \alpha > -1,\ \lambda , t \ge 0\) , satisfying the following orthogonality conditions
\(\int _{0}^{\infty } P_{m} (x; \lambda , t) P_{n}(x; \lambda , t) e^{-\lambda x} \rho _\nu (x t) x^\alpha dx = \delta _{n,m},\qquad \mathrm {(1.1)}\) 
